Given:
k = 100 lb/ft, m = 1 lb / (32.2 ft/s) = 0.03106 slugs
Solution:
F = -kx
mx" = -kx
x" + (k/m)x = 0
characteristic equation:
r^2 + k/m = 0
r = i*sqrt(k/m)
x = Asin(sqrt(k/m)t) + Bcos(sqrt(k/m)t)
ω = sqrt(k/m)
2π/T = sqrt(k/m)
T = 2π*sqrt(m/k)
T = 2π*sqrt(0.03106 slugs / 100 lb/ft)
T = 0.1107 s (period)
x(0) = 1/12 ft = 0.08333 ft
x'(0) = 0
1/12 = Asin(0) + Bcos(0)
B = 1/12 = 0.08333 ft
x' = Aω*cos(ωt) - Bω*sin(ωt)
0 = Aω*cos(0) - (1/12)ω*sin(0)
0 = Aω
A = 0
So B would be the amplitude. Therefore, the equation of motion would be x
= 0.08333*cos[(2π/0.1107)t]
The mass of a 4,900 newtons bobsled is 500 kilograms.
Answer:
question, report, observe, research, draw conclusions, hypothesize, test hypothesis, experiment
Explanation:
Explanation:
F = 20N m= m1 a=10m/s²
m=m2 a=5m/s²
F = ma
<u>for the first one</u><u>:</u><u> </u>
f=m1 × a
20 = m1 ×10
20=10m1
m1=20/10
m1=2
<u>for</u><u> </u><u>the</u><u> </u><u>second</u><u> </u><u>one</u><u> </u><u>:</u>
f=m2×a
20=m2×5
m2= 20/5
m2= 4
since F=ma
F=(m1+m2) ×a
F =(4+2)×a
F =6×a
F=20(from the question above )
20=6×a
a=20/6
a=3.33
Answer:
k_2 = 7.815 * 10^-3 s^-1
Explanation:
Given:
- rate constant of reaction k_1 = 7.8 * 10^-3 s^-1 @ T_1 = 25 C
- rate constant of reaction k_2 = ? @ T_2 = 75 C
- The activation energy E_a = 33.6 KJ/mol
- Gas constant R = 8.314472 KJ / mol . K
Find:
- rate of reaction k_2 @ T_2 = 75 C
Solution:
- we will use a combined form of Arrhenius equations that relates rate constants k as function of E_a and temperatures as follows:
k_2 = k_1 * e ^ [(E_a / R) * ( 1 / T_1 - 1 / T_2 )
- Evaluate k_2 = 7.8 * 10^-3* e^[(33.6 / 8.314472)*(1/298 -1/348)
- Hence, k_2 = 7.815 * 10^-3 s^-1
